Limit of \( \displaystyle 3 x + \left(x + 1\right)^{2} + 2 \) as \( x \to 1 \)

Problem 1.153 · medium

1. \[ \lim_{x \to 1^+}\left(3 x + \left(x + 1\right)^{2} + 2\right) \]
   limitStart with the limit of the function as x approaches 1.✓ Proved
2. \[ = \lim_{x \to 1^+}\left(x^{2} + 5 x + 3\right) \]
   algebra simplifyExpand the squared binomial term. Combine like terms.✓ Proved
3. \[ = 9 \]
   limit simplifyEvaluate the expression at x = 1. Calculate the final value.✓ Proved